Concepts

This section explains the ideas behind monoprop at a high level: the notation it uses, how problems are expressed as input, and how the propagation algorithm works. It is conceptual — for concrete constructors and arguments, see Python API.

monoprop is a classical simulator built on operator propagation. Rather than storing the full, exponentially large quantum state, it expands an operator as a real-coefficient sum of Majorana monomials and pushes that sum through a circuit one gate at a time, truncating terms that contribute little. Expectation values and gradients are then read off the propagated operator. The method is described in full in (Miller et al., 2025).

The pages below build on one another:

• Notation — the Majorana basis, monomials and their Hermitian normalisation, the commutator structure, and the paired monomials that build up a reference state. This is the vocabulary the rest of the section uses.
• Interface — how a problem is expressed: the fermionic, qubit, and Majorana operator formats, the reference state, and how a circuit is described for simulation.
• Propagation Algorithm — how propagation works: applying a gate, combining monomials, controlling term growth through truncation, and evaluating expectation values and gradients.
• Simulation modes — the Heisenberg and Schrödinger pictures: whether the observable or the state is propagated, and how to choose between them.